I read the links. But still little unclear.. Why there are differet types of waves in a single medium? Does such different waves exists in gaseous medium? I know only one wave in gases (sound wave) which has constant speed at constant fluid properties. Hope my question is not stupid.... forgive me.

A tsunami is a surface wave with a wave-length that is larger than the ocean depth.

There are two types of surface waves, deep water waves that have wave-lenghts that are small compared to the ocean depth and shallow water waves that have wave-lengths that are large compared to the depth. Sounds waves are different. Sound waves are not surface/interface waves but compression waves.

A tsunami or a shallow water wave travels with a speed propotional to the square root of g times the ocean depth, sqrt(g*d). Hence, a tsuanmi travels very fast across deep oceans - a typical speed in a typical 4000m deep ocean is around 200 m/s or 800 km/h. As the tsunami approaches land its speed is reduced as the depth is reduced.

There is no dispersion in shallow water waves or tsunamis, ie their wave-speed is not dependent on the wave-length. Normal deep-water waves are the opposite. Sounds-waves, as you mention, are also normally dispersion free and travel at a speed which is only dependent on fluid properties. You can have interface waves between different gaseous media, but the very large diffusion in gases would normally quickly destroy the interface in which the waves live and travel.

The devastating effect a tsunami has is related to the very large amount of energy they carry. When there is an earthquake on the bottom of a deep ocean all of the energy associated with dislocating the deep ocean above the earth-quake is transfered to the tsunami wave, hence, although the tsunami may look small on the surface of a deep ocean it carries a tremendous amount of energy since it involves moving the whole ocean-depth of water.

Btw, CFD Online just made a donation to Médecins Sans Frontières in support of their quick efforts to help victims in south-east asia. I urge everyone with money to spare to do the same.

Dimensionally this is correct (it gives a result in distance / time, i.e. a speed). However, I would have thought that the viscosity of the water would effect the speed. In other words, if the sea had been made of honey, the speed would be lower and if the sea had been made of alcohol, the speed would be higher.

With a length scale of 1000 km and very high fluid speeds, the Reynolds number in water is very large and viscous effects are very small as far as the large scales are concerned. Inviscid theory is a good description of the wave propagation.

The speed is dependent on the ocean depth. A typical ocean is about 4000m deep on average and a tsunami would there travel with an appoximate average speed of 200m/s (sqrt(g*4000)). In the 19th century, when it was very difficult to measure the depth of oceans, the speed of Tsunamis were actually used to estimate the depth of the oceans.

The wave-lenght varies, but each wave is normally hundreds of kilometers long. A typical tsunami wave-lenght is 200 km. That would translate into a period between each wave of 200000/200 = 1000s = 17mins. In other words, the tsunami waves would come with 17 minute intervals.

This has been a very informative message string, particularly for a technical neophyte such as myself. I have a further question, however, relating to hydrodynamics. Based on the fantastic energy transfer characteristics associated with a subsea earthquake, is it safe to presume that the building and cresting of the wave immediately prior to impact on a beach is due to the difference in velocity along the wave associated with depth? In other words, the wave piles up upon itself primarily as the rear moves more quickly than does the front, and secondarily as increasing ocean floor friction produces turbulence beneath and behind the face?

The "wave piles up upon itself" sounds like a good analogy. As a tsunami wave approaches shore the wave-speed is decreased, the wave-lenght is reduced and the wave-height is increased. The tsunami period stays the same.

Friction and turbulence plays a small role in how a tsunami moves and builds up as it approaches land, it is basically an inviscid phenomenon.

When the cause of a tsunami is sudden drop in the ocean floor due to an earth-quake the leading wave-front will be a "down" period. Hence, the first part of the tsunami to reach shore will be a wave-valley. Hence, the water will first recede due to the wave-valley before the wave-crest reaches shore.

Can you tell me if there is a general equation for approximating tsunami runup height? I found an equation on the web that equates Moment and Surface Wave Magnitudes as a basis for calcualting runup (see below), but this equation produces such an enormous difference in runup height based on variations in tsunami magnitude that I suspect it's incorrect. For example, a magnitude 8 quake produces an 8 meter runup, while a magnitude 9 quake produces a 73.5 (!) meter runup. The formula seems wrong and is certainly not supported by eye-witness estimates of the runup height of the recent Indian Ocean tsunami.

Equation:

RT = 2^MT

where

RT = Tsunami Runup Height, and MT = Tsunami Magnitude

MT is caluclated as follows:

MT = -22.6 + 3.2M

where

M = Moment Magnitude

Thank you once again, Jonas, for your patience and for sharing your expertise. I can't speak for others but I am extremely appreciative of your taking the time to teach we uninformed the rudimentary physics behind this incredibly important phenomenon.

I'm not doing research on tsunamis so I'm not the right guy to answer if there exists accurate formulas to estimate the runup height of a tsunami.

However, I really doubt if there is a general equation to estimate tsunami runup height. This is something I'd guess you need to do a detailed numerical simlation of using models that represent the geometry of the ocean floor and the shore-line in sufficient detail. An alternative is of course to correlate historical data from earlier tsunamis in the region.

Runup is a hihgly non-linear phenomena which is very dependent on the local conditions - ocean depth, shore-line shape, angle of ocean floor as it approaches the shore. Most tsunami waves do not break but behave more like a never ending flood. Wheather or not the tsunami wave breaks of course also determines how the wave-front looks.

The very large lenght-scale of tsunami waves makes them bend and diffract around obstacles like shore-lines and islands. This of course will create very warying wave-shapes and can easily cause local extrema or local minima. For example, in the recent tsunami in asia there were some islands in the maldives which were completely flooded whereas others were completely untouched although their highest point is just a meter over sea-water level.

Interesting formula btw, have you got any insight into what it is based on?

I do not know what is an origin of the equation. I would think it may have something to do with seismic wave amplitudes. The Richter scale is a logarithmic one, so the amplitude of seismic wave of 9 is 10 times the amplitude of seismic wave of 8. It looks like a simple proportionality constant close to 10, but it can be a coincidence.

I also found the equation interesting, but after further research I believe you are right: calculation of runup height is almost certainly too complex to be reduced to a general equation. The following sites offer detailed consideration of runup height and, probably, more reasonably appreciate in their calculations the breadth of variables required for solid prediction.

Energy of a seismic wave is proportional to power 2 of amplitude, thus the energy of the wave of 9 is 100 times the energy of the wave of 8. Part of this energy is dissipated in earh (rocks) and part is transfer to a tsunami. I think there is no simple answer to the question of how much energy is lost and how much reach a shore.